What is Solved Examples Of Binomial Theorem- 1

If a die is thrown 5 times, what is the chance that an even number will come up exactly 3 times?

Sol.

When a die is thrown once, let S be the sample space and E the event of occurrence of an even number, then

S = {1, 2, 3, 4, 5, 6} \ n(S) = 6 and E = P{2, 4, 6} \ n(E) = 3

The die has been thrown 5 time, therefore number of trials n = 5

Now p = probability of occurrence of event E in one trial

Now probability of occurrence of an even number exactly 3 times in 5 trials

P(X = 3) or P(3) = 5C3p3q2 = 5 / 3 / 2 (1/2)3.(1/2)2 = 10/32 = 5/16

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